Here's an observation that might lead to a quick way to determine unique bucket combinations.

The set of bucket sizes above is the union of two sets: the set of all unique arrangements of (1 1 1 3), and the set of all unique arrangements of (1 1 2 2). The sum of the numbers is equal to the number of catagories. This can be generalized to cover different numbers of buckets and different numbers of categories.

In reply to Re: Re: Puzzle: need a more general algorithm by dws
in thread Puzzle: need a more general algorithm by Ovid

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